It's a linear regulator, so the power (and heat) depends on the volatage dropped across the regulator and the current through it. If you are powering the board from 7V (with 2V dropped across the regulator) you can get more current than if you are powering the board from 12V (with 7V dropped across the regulator).

Itr also depends on what your Arduino is powering... If you've got a bunch of LEDs connected to the Arduino's outputs, that means less "extra" current avaliable for your other circuitry.

Up to 800mA thru the 5V regulator with a low voltage source, as DVDdoug says.http://www.digikey.com/product-detail/en/LM1117MPX-5.0%2FNOPB/LM1117MPX-5.0%2FNOPBCT-ND/660149

http://www.dipmicro.com/store/DCA-07510Above that voltage, you need to worry about overheating.Out of that 800, the Mega 2560 uC uses some, the USB/Serial uses some, the 3.3V regulator uses some, whatever IO you are driving uses some ...So probably on the order of 700mA if you have little to no IO using energy.

If powering from the USB port, the starting number is 500mA, limited by USB port and the onboard 500mA PTC resettable fuse.